Properties of Matter
What this domain tests
Properties of Matter tests elasticity (stress, strain, Young's modulus, elastic potential energy), surface tension, viscosity, terminal velocity and Bernoulli's principle.
Core rules
- Stress = force/area; strain = change in dimension/original dimension; Young's modulus Y = (F/A)/(ΔL/L).
- Elastic PE per unit volume = ½ × stress × strain.
- Surface tension S = force/length; excess pressure inside a soap bubble = 4S/r, inside a liquid drop = 2S/r.
- Viscous force F = 6πηrv (Stokes); terminal velocity v_t = 2r²(ρ − σ)g/(9η).
- Bernoulli: P + ½ρv² + ρgh = constant along a streamline for steady, non-viscous, incompressible flow.
Worked example
A wire of length 2.0 m and cross-sectional area 1.0 × 10⁻⁶ m² extends by 1.0 mm under a load of 100 N. Y = FL/(AΔL) = (100 × 2.0)/(1.0 × 10⁻⁶ × 1.0 × 10⁻³) = 2.0 × 10¹¹ Pa. The extension must be converted to metres; keeping it in mm gives an answer 1000 times too large.
Traps
Using diameter instead of radius in area; forgetting that a needle or wire has two surfaces when surface tension acts; using gauge pressure instead of total pressure in Bernoulli; applying Bernoulli to viscous or turbulent flow; mixing up ρ (body) and σ (fluid) in terminal velocity.